We determine exactly the expected number of hamilton cycles in the random graph obtained by starting with n isolated vertices and adding edges at random until each vertex degree is at least two. This complements recent work of Cooper and Frieze. There are similar results concerning expected numbers for example of perfect matchings, spanning trees, hamilton paths and directed hamilton cycles.

We study a Fermi Hamilton operator K̂ which does not commute with the number operator N̂ . The eigenvalue problem and the Schrödinger equation is solved. Entanglement is also discussed. Furthermore the Lie algebra generated by the two terms of the Hamilton operator is derived and the Lie algebra generated by the Hamilton operator and the number operator is also classified.

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

In this paper we investigate Donder-Weyl (DW) Hamilton-Jacobi equations and establish the connection between DW Hamilton-Jacobi equations and multi-symplectic Hamiltonian systems. Based on the study of DW Hamilton-Jacobi equations, we present the generating functions for multi-symplectic partitioned Runge-Kutta (PRK) methods.

Department of Psychology, Neuroscience and Behaviour, McMaster University, Hamilton, ON, Canada L8S 4K1; Martinos Center for Biomedical Imaging, Harvard Medical School/Massachusetts General Hospital, Boston, MA 02129; McMaster Institute for Music and the Mind, Hamilton, ON, Canada L8S 4K1; Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada L8S 4K1; and ...

A Hamilton cycle is a cycle containing every vertex of a graph. A graph is called Hamiltonian if it contains a Hamilton cycle. The Hamilton cycle problem is to find the sufficient and necessary condition that a graph is Hamiltonian. In this paper, we give out some new kind of definitions of the subgraphs and determine the Hamiltoncity of edges according to the existence of the subgraphs in a gr...